In this section, we give a mathematical formulation of a computing machine based on algebra and geometry. First, we formulate a machine as a framed module over an algebra, together with a metric on the module and a collection of non-linear functions. Second, we take into account of isomorphisms of framed modules and make sure the construction is equivariant under the automorphism group, and hence descends to the moduli stack of framed modules. Finally, we extend the noncommutative geometry developed by [1]}, [2]}, [3]} to the context of near-rings, and show how it fits into this framework.
